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The centre of the mass of \(3\) particles, \(10\) kg, \(20\) kg, and \(30\) kg, is at \((0,0,0)\). Where should a particle with a mass of \(40\) kg be placed so that its combined centre of mass is \((3,3,3)\)?

1. \((0,0,0)\)

2. \((7.5, 7.5, 7.5)\)

3. \((1,2,3)\)

4. \((4,4,4)\)

Subtopic: Center of Mass |

76%

From NCERT

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The position of a particle is given by \(\vec r = \hat i+2\hat j-\hat k\) and momentum \(\vec P = (3 \hat i + 4\hat j - 2\hat k)\). The angular momentum is perpendicular to:

1. | X-axis |

2. | Y-axis |

3. | Z-axis |

4. | Line at equal angles to all the three axes |

Subtopic: Angular Momentum |

63%

From NCERT

PMT - 2000

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A wheel with a radius of \(20\) cm has forces applied to it as shown in the figure. The torque produced by the forces of \(4\) N at \(A\), \(8~\)N at \(B\), \(6\) N at \(C\), and \(9~\)N at \(D\), at the angles indicated, is:

1. \(5.4\) N-m anticlockwise

2. \(1.80\) N-m clockwise

3. \(2.0\) N-m clockwise

4. \(3.6\) N-m clockwise

Subtopic: Torque |

77%

From NCERT

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A particle of mass \(m\) moves in the\(XY\) plane
with a velocity of \(v\) along the straight line \(AB.\) If the angular momentum of the particle about the origin \(O\) is \(L_A\)_{ }when it is at \(A\) and \(L_B\)_{ }when it is at \(B,\) then:

1. | \(L_A>L_B\) |

2. | \(L_A=L_B\) |

3. | The relationship between \(L_A\) and \(L_B\) depends upon the slope of the line \(AB.\) |

4. | \(L_A<L_B\) |

Subtopic: Angular Momentum |

65%

From NCERT

AIIMS - 2007

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A wheel is rotating about an axis through its centre at \(720\) r.p.m. It is acted upon by a constant torque opposing its motion for \(8\) seconds to bring it to rest finally.
The value of torque in N-m is: (given \(I\) = $\frac{24}{\mathrm{\pi}}$ kg ${\mathrm{m}}^{2}$)

1. \(48\)

2. \(72\)

3. \(96\)

4. \(120\)

Subtopic: Rotational Motion: Dynamics |

84%

From NCERT

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For L = 3.0 m, the total torque about pivot A provided by the forces as shown in the figure is:

1. | 210 Nm | 2. | 140 Nm |

3. | 95 Nm | 4. | 75 Nm |

Subtopic: Torque |

59%

From NCERT

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Two rotating bodies \(A\) and \(B\) of masses \(m\) and \(2m\) with moments of inertia ${I}_{A}$ and ${I}_{B}({I}_{B}{I}_{A})$ have equal kinetic energy of rotation. If ${L}_{A}$ $$and ${L}_{B}$ be their angular momenta respectively, then:

1. ${L}_{A}=\frac{{L}_{B}}{2}$

2. ${L}_{A}=2{L}_{B}$

3. ${L}_{B}>{L}_{A}$

4. ${L}_{A}>{L}_{B}$

Subtopic: Rotational Motion: Dynamics |

71%

From NCERT

NEET - 2016

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The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through:

1. B

2. C

3. D

4. A

Subtopic: Moment of Inertia |

79%

From NCERT

NEET - 2012

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A light rod of length \(l\) has two masses, \(m_1\) and \(m_2,\) attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is:

1. \(\frac{m_1m_2}{m_1+m_2}l^2\)

2. \(\frac{m_1+m_2}{m_1m_2}l^2\)

3. \((m_1+m_2)l^2\)

4. \(\sqrt{(m_1m_2)}l^2\)

1. \(\frac{m_1m_2}{m_1+m_2}l^2\)

2. \(\frac{m_1+m_2}{m_1m_2}l^2\)

3. \((m_1+m_2)l^2\)

4. \(\sqrt{(m_1m_2)}l^2\)

Subtopic: Moment of Inertia |

75%

From NCERT

NEET - 2016

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A rod of weight \(w\) is supported by two parallel knife edges, \(A\) and \(B\), and is in equilibrium in a horizontal position. The knives are at a distance \(d\) from each other. The centre of mass of the rod is at a distance \(x \) from \(A\). The normal reaction on \(A\) is:

1. | \(wx \over d\) | 2. | \(wd \over x\) |

3. | \(w(d-x) \over x\) | 4. | \(w(d-x) \over d\) |

Subtopic: Torque |

67%

From NCERT

NEET - 2015

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